PoS(QNP2012)032 http://pos.sissa.it/ anniversary of QCD, “QCD–XL” th † ∗ [email protected] Speaker. On leave of absence: St. Petersburg Nuclear Physics Institute, Gatchina, Russia. Some remarks on the 40 ∗ † Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. c

Sixth International Conference on Quarks andApril Nuclear 16-20, Physics, 2012 Ecole Polytechnique, Palaiseau, Paris LPTHE, University Paris-VI and CNRS, Paris,E-mail: France Yu.L. Dokshitzer Concluding remarks PoS(QNP2012)032 the was Omega turns into the t Yu.L. Dokshitzer increases catas- , the unitary group ) -baryon was discov- 3 ( Ω SU ” (1962). ]. 1 2 the correct meson theory will not be found in the next . In the crossing channel, the momentum transfer 2 k . The error was found (B. Ioffe and A. Galanin) and the write-up of the = t ), and the imaginary part of the loop is proportional to the cross section of s (1960). This harsh statement resulted from a traumatic experience that followed ”. at large momentum scales (small distances) [ of the New Times — the first true “Ahaa!” of the Quark Model. (The final — decisive asymptotic freedom If the information I’ve heard is really right, then our speculation might have some value, On the theory side, that wasBack a in 3D decade: 1958, one Freeman of Dyson Despair, (the Distrust and great Diversions. man who has always argued that “itThe is depth better of despair to can be be gauged by the famous punch-line belonging to : “ Recall that it is the vacuum polarization electron loop in the photon polarization operator that Landau had a good reason to believe that this phenomenon applies to effective coupling in any At the end of one plenary session on strange-, Gell-Mann strode to the micro- In the early 1960’s the particle garden has started to turn into jungles. The baryons and mesons Alpha the — “Ahaa!” came with the discovery of the 4th quark 10 years later.) 2. Theoretical Background wrong than to be vague”)hundred years professed that “ Hamiltonian method for strong interactionsdeserved is honor dead and must be buried, although of course with trophically makes the effective chargethe run momentum with transfer, virtuality.annihilation As energy any ( QFT amplitude, this loop is analytic in the discovery of “nullification” of(aka the “ zero”). effective interaction In 1954 strength Abrikosov inlogarithmic and approximation”, Quantum Khalatnikov, have equipped Electrodynamics performed by the Landau’s first idea calculation ofrunning of “leading electron the running mass electric in charge and QED and found that the effective interaction strength paper corrected (before publication). Thethree-year-long profound blow search was (1955-58) so which hard hasof that lead the him Isaak coupling to Pomeranchuk was conclude undertook a that general, a QED-ish seemingly behavior inevitable property of any QFT. (QFT). Actually,authors the have initial obtained a calculation “QCD-ish” contained beta-function! a Forenthusiastically a wrong discussed couple with sign of their weeks so pupils Landau a that and beautiful Pomeranchuk the physicalyou picture probe of the charge electron disappearing when closer andcall closer now to its “core”... The picture has been developed of what we of dimension 3 — wasMann proposed “The independently Eightfold by Way”. Gell-Mann and Ne’eman and named byphone: Gell- “ and we should look for the lastered particles, in called, 1964 say, Omega-minus by aUniversity team using of the 80-inch from bubble Brookhaven, chamber the at University Brookhaven’s AGS. of The Rochester discovery and of Syracuse QCD-XL 1. Phenomenological Background known at the timequantum fell numbers (spin into and parity), symmetric but differing familiesand in an strangeness. of ordered The way multiplets in mathematical mass, (octuplets, group charge, to baryon decuplets) fit number sharing this complex two situation — PoS(QNP2012)032 ]. 3 Yu.L. Dokshitzer ] left the following milestones on the 2 3 . These are words from the paper “Advantages of the Color Octet Gluon ]. Its abstract read: “It is pointed out that there are several advantages in abstracting 4 a Lagrangian field theory model in which quark fields are coupled symmetrically to a “Scaling regime”, and the breakthrough in the theory of second order phase transitions [ Singularities of these partial wavesin drive the the crossing high channel, energy behavior of scattering amplitudes “” as the leading singularity in the vacuum channel, Interacting as the first example of intrinsic dynamical instability “in the infrared”, Analytic continuation of partialmentum, wave amplitudes onto complex values of the angular mo- Unitarity and its analytic continuation into crossing channels (Mandelstam), Growth of the hadron interaction radiusCausality with and collision Relativity energy (Gribov). as a consequence of Unitarity, Exploration of Analytic properties of scattering amplitudes (Dispersion relations), Crossing as specific feature of relativistic theory, “Bootstrap” and the birth of String Theory (Veneziano amplitude), Detailed scrutiny of the relativistic scattering theory (Pomeranchuk theorem. Froissart bound), — Among Fritzsch–Gell-Mann–Leutwyler commandments were: Not having much trust in microscopic dynamics, in the late 50’s–60’s theorists undertook a This path has lead to understanding of many a deep features of relativistic dynamics: • • • • • • • • • • • 3. QCD neutral vector “gluon” field Picture” [ properties of hadrons and theirand currents color from octet a gluons.” Yang–Mills gauge model based on colored quarks The Gribov–Regge theory of complexroad angular to understanding momenta hadron [ interactions at very high energies: QCD-XL production of the pair.of The the latter logarithm got in toimpossible. be the positive running As (unitarity), coupling, and a thus thiscausality result, (analyticity), dictates making relativistic the the crossing the ‘Moscow sign and “asymptotically unitarity. zero” free” seemed behavior to look be an inevitable direct consequenceflanking maneuver. of The emphasis wasas put on on abstracting studying properties general of structuremany the of (an scattering a infinite matrix, theory number as of) of well particles strong — interactions hadrons that and would hadron be resonances. able to embed PoS(QNP2012)032 to give the Yu.L. Dokshitzer in addition to the 0 u fluctuations, was signaling t high frequencies k groups 3 SU 4 may be necessary so as to confine the quarks and and the color 3 SU ]. 5 low frequencies , there are still three colors and the principal conclusions set forth here are s and d , u no mixing between the usual “the bare coupling constant is zero” (referring to Politzer,axial Gross anomaly & and Wilczek the 1973 absence preprints) of the 9th massless pseudoscalar meson in the chiral limit the gluons are now just as fictitious as thehint quarks as to why Nature selects color singlets (We should mention that even if there isunaffected.) a fourth “charmed” quark Thus, we do not acceptallow any theories scheme in in which which the quarks color are non-singlet degrees real,Color of observable is freedom particles; a can perfect be nor symmetry. excited. do we The quarks come in three “colors”,singlets but all with physical respect states to and the interactions SU are of supposed color. to be usual Likewise a modification at So, the microscopic dynamics underlying the physics of hadrons was formulated in its entirety If we accept the stronger abstractions like exact asymptotic Bjorken scaling, we may have • • • • 3. 4. 5. 1. 2. antiquarks permanently inside the hadrons. Very well may be. This remains an open question, after all theseand years. complexity. Thanks to QCD, themultitude QFT of has problems re-established of itself hadrons asto and an applications. their adequate interactions. approach The to 40 the years that followed were devoted A number of hints fromthe high fact energy that phenomenology in could high havescattering energy been hinted hadron added at interaction to proton processes the being inelastictransverse list. a breakup momenta loosely Namely, dominates of bound over produced compound elastic hadrons, objectthe rare (constituent weakness quarks). appearance of of interaction Limited large- atwith small energy relative of distances total hadron (asymptotic interaction freedom).of cross produced sections, Practical hadrons Feynman hinted constancy rapidity at plateau vectorapplied (spin in the 1) the nature notion distribution of of the a mediating mediating field, elementary should particleQuote/Unquote one to dare strong to interactions have (gluon). to assume that thetransverse propagation momentum cutoff. of gluons isActually, somehow the modified authors did at it not had have to been accept understooddimensionless such that coupling a constant the [ “stronger Bjorken abstraction”: scaling already scaling at could that not time hold exactly in a QFT with Describing the advantages of havingreasons: 8 gluons rather than 1, the authors have listed the following QCD-XL PoS(QNP2012)032 (4.1) with respect one-line-all- and is different Yu.L. Dokshitzer ) 4 SYM share the x ( (1954) 497, 773, = O N 95 universal . that matters. It is the essence  ) A x ( O (integrable) field model. Recent the- + x x − 0), nor in parton multiplication (no second 1 ≡  ) ). s α α ] which states that soft gluon radiation has in fact 5 ( π A 7 4.1 β C fully solvable = in perturbation theory (provided the “physical scheme” ) x ( g 4 Super-Symmetric Yang-Mills (SYM) model. + 4 SYM QFT should provide us one day with a A = ]. → = N 8 A ) N all orders x ( P holds in . At the same time, the first — “classical” — term is A 4.1 . It is independent of the quantum state of the radiating parton system, and does not ]. QCD would benefit a lot from such a solution, since QCD and 6 4 SYM has a good chance to be a = description of the major part of the QCD parton dynamics. L.D. Landau, A.A. Abrikosov and I.M.1177. Khalatnikov, Dokl. Akad. Nauk SSSR V.N. Gribov, “Strong interactions of hadrons atUniv. Pr., high Yu.L. emnergies: Dokshitzer, J. Gribov Nyiri, lectures (ed.), on”, 2009, Cambridge 477 p. Taken globally, the rôle of fermion and scalar fields present in the Lagrangian of the model The gluon radiation probability has, in general, two terms: “classical” and “quantum”: A complete solution of the QCD is on the move. But the driving motivations have changed. No-one is interested any Physics of hadrons has never been simple. And will never be. At the same time, an explosive Having claimed upper hand in hadron physics 40 years ago, QFT has now aN good chance to [1] [2] for the QCD coupling is chosen) [ classical nature The second — “quantum” — term, vanishes in the small gluon energy limit as change it. The Eq. consists of canceling effects of “quantum” gluons.selves As neither a in result, the quantum corrections running manifest of them- the coupling ( oretical developments hint at anat intriguing the possibility quantum that level, this mayoperators QFT, admit [ super-conformally an invariant all loopgluon solution sector. for anomalous dimensions of its composite for different emitters to intrinsic quantum properties ofprocess: participating objects it and is the only natureof of classical the the movement celebrated underlying of Low–Burnett–Kroll scattering the theorem [ “charged particle” term in the one-loop anomalous dimension Eq. order References QCD-XL 4. QCD on the move longer in “checking” QCD. Now theget goal deeper. is “Bump to Hunting” learn is howfor still to unconventional an apply objects, actuality, it, as one to it looks precise,conditions was to for like in go HI unconventional pre-QCD broader collisions. behavior epoch. and by As putting well QCD as into looking extreme progress in analytic calculations of multi-legyears QFT provides amplitudes reappearing and themes, multi-loop motives, corrections constructs,deep in of structure recent striking of simplicity. the Could underlying it QFT dynamics be is that actually the simpler thanamuse one us dared with to a think? new breakthrough.of It its should most arise symmetric from a child deeper — scrutiny the of the algebraic structure PoS(QNP2012)032 (1968) 86. (2004) 4715. Yu.L. Dokshitzer 20 A 19 (1973) 365. B47 (2007) 189. (1972) 438, 675. 15 B646 6 (1958) 974; T.H. Burnett and N.M. Kroll, Phys. Rev. Lett. 110 Yu.L. Dokshitzer and G. Marchesini, Phys. Lett. M. Gell-Mann, G. Fritzsch and H. Leutwyler, Phys.V.N. Lett. Gribov and L.N. Lipatov, Sov. J. Nucl. Phys. A.V. Belitsky, V.M. Braun, A.S. Gorsky and G.P. Korchemsky, Int.F.E. J. Low, Mod. Phys. Phys. Rev. A. Polyakov, “A view form the Island”, arXiv: hep-th/9211140. [8] [4] [5] [6] [7] [3] QCD-XL